The oscillatory character of the recursive sequence xn+1=α+βxn-k+1A+Bxn-2k+1

The aim of this work is to generalize techniques of difference equations in order to apply them to a wider class. We start by establishing the boundedness, the oscillatory character, and the global stability of the equationxn+1=α+βxn-k+1A+Bxn-2k+1,n=0,1,2,…with positive parameters, k ∈ {1, 2, …}, and nonnegative initial conditions.